@article{Maksimenko_Feshchenko_2014, title={Homotopic Properties of the Spaces of Smooth Functions on a 2-Torus}, volume={66}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2211}, abstractNote={Let <em class="a-plus-plus">f</em> : <em class="a-plus-plus">T</em> <sup class="a-plus-plus">2</sup> → ℝ be a Morse function on a 2-torus, let <em class="a-plus-plus">S</em>(<em class="a-plus-plus">f</em>) and <span class="a-plus-plus inline-equation id-i-eq1"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{O} \)</span> </span>(<em class="a-plus-plus">f</em>) be, respectively, its stabilizer and orbit with respect to the right action of the group <span class="a-plus-plus inline-equation id-i-eq2"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{D} \)</span> </span>(<em class="a-plus-plus">T</em> <sup class="a-plus-plus">2</sup>) of diffeomorphisms of <em class="a-plus-plus">T</em> <sup class="a-plus-plus">2</sup>, let <span class="a-plus-plus inline-equation id-i-eq3"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{D} \)</span> </span> <sub class="a-plus-plus">id</sub>(<em class="a-plus-plus">T</em> <sup class="a-plus-plus">2</sup>), be the identity path component of the group <span class="a-plus-plus inline-equation id-i-eq4"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{D} \)</span> </span>(<em class="a-plus-plus">T</em> <sup class="a-plus-plus">2</sup>), and let <em class="a-plus-plus">S</em>′(<em class="a-plus-plus">f</em>) = <em class="a-plus-plus">S</em>(<em class="a-plus-plus">f</em>) ∩ <span class="a-plus-plus inline-equation id-i-eq5"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{D} \)</span> </span> <sub class="a-plus-plus">id</sub>(<em class="a-plus-plus">T</em> <sup class="a-plus-plus">2</sup>). We present sufficient conditions under which <span class="a-plus-plus equation id-equa"> <span class="a-plus-plus equation-source format-t-e-x">$$ {\uppi}_1\mathcal{O}(f)={\uppi}_1{\mathcal{D }_{\mathrm{id }\left({T}^2\right)\times {\uppi}_0S^{\prime }(f)\equiv {\mathrm{\mathbb{Z }^2\times {\uppi}_0S^{\prime }(f). $$</span> </span&gt; The obtained result is true for a larger class of functions whose critical points are equivalent to homogeneous polynomials without multiple factors.}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Maksimenko, S. I. and Feshchenko, B. G.}, year={2014}, month={Sep.}, pages={1205–1212} }